In this paper, the intermolecular structural study asserted by the vibrational analysis in the stretch frequencies of hydrogen bonds (π⋯H) and dihydrogen bonds (H−δ⋯H+δ) have definitively been revisited by means of calculations carried out by Density Functional Theory (DFT) and topological parameters derived from the classic treatise of the Quantum Theory of Atoms in Molecules (QTAIM). As a matter of fact the π⋯H hydrogen bond is formed between the hydrofluoric acid and the CC bond of the acetylene, but the QTAIM calculations revealed a distortion in this interaction due to the formation of the ternary complex C2H2⋯2(HF). Although the π bonds of ethylene (C2H4), propylene (C2H3(CH3)), and t-butylene (C2H2(CH3)2) are considered proton acceptors, two hydrogen-bond types—π⋯H and C⋯H—can be observed. Over and above the analysis of the π hydrogen bonds, theoretical arguments also were used to discuss the red-shifts in the stretch frequencies of the binary dihydrogen complexes formed by BeH2⋯HX with X = F, Cl, CN, and CCH. Although a vibrational blue-shift in the stretch frequency of the H–C bond of HCF3 due to the formation of the BeH2⋯HCF3 dihydrogen complex was obtained, unmistakable red-shifts were detected in LiH⋯HCF3, MgH2⋯HCF3, and NaH⋯HCF3. Moreover, the alkali–halogen bonds were identified in relation to the formation of the trimolecular systems NaH⋯2(HCF3) and NaH⋯2(HCCl3). At last, theoretical calculations and QTAIM molecular integrations were used to study a novel class of dihydrogen-bonded complexes (mC2H5+ ⋯nMgH2 with m = 1 or 2 and n = 1 or 2) based in the insight that MgH2 can bind with the non-localized hydrogen H+δ of the ethyl cation (C2H5+). In an overview, QTAIM calculations were applied to evaluate the molecular topography, charge density, as well as to interpret the shifted frequencies either to red or blue caused by the formation of the hydrogen bonds and dihydrogen bonds.